King Abdullah and Hosni Mubarak, the Egyptian president, are worried about the prospects for Arab-Israeli peace after the election of a new Israeli government under Ehud Olmert and a new Palestinian government led by Hamas.
Olmert says he aims to set Israel's borders unilaterally if no basis can be found for negotiations - a prospect that seems remote since Hamas is sworn to Israel's destruction and has refused to sign up to existing interim peace deals.
After a summit in the Red Sea port of Aqaba, Ahmed Aboul Gheit, the Egyptian foreign minister, and his Jordanian counterpart Abdelelah al-Khatib, said they would lobby a meeting of the Middle East Quartet in New York on May 9.
The Quartet comprises the United Nations, the European Union, the United States and Russia. Jordan and Egypt are to attend as regional partners from the Middle East.
Said al-Khatib: "We believe the coming meeting of the Quartet to be very important and timely and coming after a long suspension of the peace process which faces a difficult period.
"There ought to be international efforts to push forward the peace process away from unilateral steps and a return to the negotiating table"
Jordanian foreign minister
"There ought to be international efforts to push forward the peace process away from unilateral steps and a return to the negotiating table."
The Quartet backs a negotiated two-state solution, but its road map for arriving there has been wrecked by many months of violence and increasing intransigence.
Egypt and Jordan, which both have peace treaties and diplomatic relations with Israel, want the Hamas-led Palestinian government to accept a 2002 Arab peace initiative.
This offers Israel peace and normal ties in exchange for withdrawal from land occupied in the Middle East war of 1967.